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Matrix congruence is an equivalence relation. Matrix congruence arises when considering the effect of change of basis on the Gram matrix attached to a bilinear form or quadratic form on a finite-dimensional vector space : two matrices are congruent if and only if they represent the same bilinear form with respect to different bases .
The Cayley–Purser algorithm was a public-key cryptography algorithm published in early 1999 by 16-year-old Irishwoman Sarah Flannery, based on an unpublished work by Michael Purser, founder of Baltimore Technologies, a Dublin data security company. Flannery named it for mathematician Arthur Cayley. It has since been found to be flawed as a ...
The Encyclopedia of Cryptography and Security is a comprehensive work on Cryptography for both information security professionals and experts in the fields of Computer Science, Applied Mathematics, Engineering, Information Theory, Data Encryption, etc. [1] It consists of 460 articles in alphabetical order and is available electronically and in print.
The following outline is provided as an overview of and topical guide to cryptography: Cryptography (or cryptology) – practice and study of hiding information. Modern cryptography intersects the disciplines of mathematics, computer science, and engineering. Applications of cryptography include ATM cards, computer passwords, and electronic ...
Secret sharing consists of recovering a secret S from a set of shares, each containing partial information about the secret. The Chinese remainder theorem (CRT) states that for a given system of simultaneous congruence equations, the solution is unique in some Z/nZ, with n > 0 under some appropriate conditions on the congruences.
Mathematically, a cryptosystem or encryption scheme can be defined as a tuple (,,,,) with the following properties.. is a set called the "plaintext space". Its elements are called plaintexts.; is a set called the "ciphertext space". Its elements are called ciphertexts.; is a set called the "key space". Its elements are called keys.; = {:} is a set of functions :. Its elements are called ...
Hill's cipher machine, from figure 4 of the patent. In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra.Invented by Lester S. Hill in 1929, it was the first polygraphic cipher in which it was practical (though barely) to operate on more than three symbols at once.
The algorithm has never gained much acceptance in the cryptographic community, but is a candidate for "post-quantum cryptography", as it is immune to attacks using Shor's algorithm and – more generally – measuring coset states using Fourier sampling.